Solve. displaystyleintfrac{{{78}{x}}}{{{25}-{12}{x}+{4}{x}^{2}}}

banganX 2020-12-15 Answered
Solve. 78x2512x+4x2
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Expert Answer

SoosteethicU
Answered 2020-12-16 Author has 102 answers
The given integration is
78x2512x+4x2
A simple calculation the integration becomes
78x2512x+4x2=7dx2512x+4x2
=7dx4x212x+25
=7dx4(x23x+254)
=74dxx23x+254
=74dxx23x+254
=74dxx22x32+94+25494
=74dx(x32)2+164
=74dx(x32)2+(2)2
=74×12tan1(x322)+C
[By using the formula dxx2+a2=1atan1(xa)+C]
=78tan1(2x34)+C
Where C is the constant of integration.
Thus, the value of the integration is
7dx2512x+4x2=78tan1(2x34)+C
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